Majorana fermions often coexist with other low-energy fermionic degrees of freedom. In such a situation, topological quantum computation requires the use of fermionic zero modes of a many-body system. We classify all such modes for interacting fermions and show how to select the mode that maximizes the decoherence time. We find that in a typical interacting system the maximal decoherence time is within one order of magnitude from the decoherence time of a qubit based on the local part of the fermion parity operator.

• Received 4 December 2013
• Revised 8 January 2014

DOI:https://doi.org/10.1103/PhysRevB.89.035136